Details

analyze145.0ms (3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 32 to 22 computations (31.3% saved)

sample26.0ms (0.5%)

Algorithm

1×

intervals

Results

17.0ms

256×

body

128

valid

Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify235.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4912	46
1	4912	46

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.2b

Counts

2 → 1

Compiler

Compiled 62 to 42 computations (32.3% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
0.1b	(.f64 (.f64 a a) (+.f64 1 a))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
1.3b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

rewrite44.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-exp-log_binary64_2525` `pow1_binary64_2548`
14×	`add-cbrt-cube_binary64_2523`
10×	`*-un-lft-identity_binary64_2487` `add-sqr-sqrt_binary64_2509`
8×	`add-cube-cbrt_binary64_2522`
7×	`associate-r_binary64_2427`
6×	`prod-exp_binary64_2536` `cbrt-unprod_binary64_2520` `pow-prod-down_binary64_2558` `add-log-exp_binary64_2526`
4×	`distribute-rgt-in_binary64_2437` `distribute-lft-in_binary64_2436` `associate-*r/_binary64_2429`
3×	`pow-unpow_binary64_2564` `unpow-prod-down_binary64_2566`
2×	`unswap-sqr_binary64_2455` `sub-neg_binary64_2480` `-commutative_binary64_2418` `cancel-sign-sub-inv_binary64_2453` `flip-+_binary64_2461` `flip3-+_binary64_2490` `associate-+r+_binary64_2419` `associate-l*_binary64_2428`
1×	`pow-exp_binary64_2555` `flip--_binary64_2462` `pow-to-exp_binary64_2556` `pow-pow_binary64_2559` `distribute-lft-out_binary64_2438` `+-commutative_binary64_2417` `sum-log_binary64_2578` `sqr-pow_binary64_2459` `unpow2_binary64_2552` `flip3--_binary64_2491`

Counts

4 → 80

Calls

4 calls:

10.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
10.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
9.0ms	(.f64 (.f64 a a) (+.f64 1 a))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series332.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

145.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
69.0ms	(.f64 (.f64 a a) (+.f64 1 a))
66.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
52.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify43.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5113	1848

prune211.0ms (4.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	2	93

Merged error: 0.0b

Counts

93 → 2

Compiler

Compiled 5047 to 2892 computations (42.7% saved)

localize23.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 b b) (.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
0.1b	(.f64 (.f64 a a) (+.f64 1 a))
1.3b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
2.8b	(.f64 (.f64 b b) (*.f64 a a))

rewrite83.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`pow1_binary64_2548`
32×	`associate-*r/_binary64_2429`
26×	`add-exp-log_binary64_2525` `add-cbrt-cube_binary64_2523`
20×	`pow-prod-down_binary64_2558` `frac-add_binary64_2495`
14×	`prod-exp_binary64_2536` `flip-+_binary64_2461` `flip3-+_binary64_2490` `cbrt-unprod_binary64_2520`
13×	`add-log-exp_binary64_2526`
8×	`-un-lft-identity_binary64_2487` `add-sqr-sqrt_binary64_2509` `associate-r*_binary64_2427`
6×	`add-cube-cbrt_binary64_2522` `sum-log_binary64_2578`
5×	`flip--_binary64_2462` `flip3--_binary64_2491`
4×	`distribute-rgt-in_binary64_2437` `distribute-lft-in_binary64_2436` `pow-plus_binary64_2550` `pow-prod-up_binary64_2557`
3×	`unswap-sqr_binary64_2455` `-commutative_binary64_2418` `associate-l*_binary64_2428`
2×	`sub-neg_binary64_2480` `cancel-sign-sub-inv_binary64_2453` `pow-sqr_binary64_2460` `pow2_binary64_2568` `associate-+r+_binary64_2419`
1×	`associate-+l+_binary64_2420` `distribute-lft-out_binary64_2438` `+-commutative_binary64_2417`

Counts

4 → 106

Calls

4 calls:

33.0ms	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 b b) (.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
10.0ms	(.f64 (.f64 b b) (*.f64 a a))
10.0ms	(.f64 (.f64 a a) (+.f64 1 a))
9.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

series316.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

131.0ms	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 b b) (.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
73.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
66.0ms	(.f64 (.f64 a a) (+.f64 1 a))
45.0ms	(.f64 (.f64 b b) (*.f64 a a))

simplify105.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4936	4777
1	4936	4777

prune306.0ms (6.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	118	2	120

Merged error: 0.0b

Counts

120 → 2

Compiler

Compiled 6605 to 4026 computations (39% saved)

localize23.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 2 (pow.f64 (.f64 b a) 2)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
0.1b	(.f64 (.f64 a a) (+.f64 1 a))
0.1b	(pow.f64 (*.f64 b a) 2)
1.3b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

rewrite66.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`associate-*r/_binary64_2429`
20×	`frac-add_binary64_2495`
17×	`add-exp-log_binary64_2525` `pow1_binary64_2548`
14×	`flip-+_binary64_2461` `flip3-+_binary64_2490` `add-cbrt-cube_binary64_2523`
13×	`add-log-exp_binary64_2526`
9×	`*-un-lft-identity_binary64_2487` `add-sqr-sqrt_binary64_2509`
7×	`prod-exp_binary64_2536` `add-cube-cbrt_binary64_2522` `pow-prod-down_binary64_2558` `associate-r_binary64_2427`
6×	`sum-log_binary64_2578` `cbrt-unprod_binary64_2520`
5×	`flip--_binary64_2462` `flip3--_binary64_2491`
4×	`distribute-rgt-in_binary64_2437` `distribute-lft-in_binary64_2436`
3×	`pow-unpow_binary64_2564`
2×	`pow-exp_binary64_2555` `unswap-sqr_binary64_2455` `sub-neg_binary64_2480` `-commutative_binary64_2418` `cancel-sign-sub-inv_binary64_2453` `pow-pow_binary64_2559` `associate-+r+_binary64_2419` `associate-l*_binary64_2428`
1×	`associate-+l+_binary64_2420` `unpow-prod-down_binary64_2566` `pow-to-exp_binary64_2556` `distribute-lft-out_binary64_2438` `+-commutative_binary64_2417` `sqr-pow_binary64_2459` `unpow2_binary64_2552`

Counts

4 → 95

Calls

4 calls:

22.0ms	(+.f64 (+.f64 (.f64 2 (pow.f64 (.f64 b a) 2)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
11.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
10.0ms	(.f64 (.f64 a a) (+.f64 1 a))
5.0ms	(pow.f64 (*.f64 b a) 2)

series315.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

134.0ms	(+.f64 (+.f64 (.f64 2 (pow.f64 (.f64 b a) 2)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
74.0ms	(.f64 (.f64 a a) (+.f64 1 a))
65.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
41.0ms	(pow.f64 (*.f64 b a) 2)

simplify78.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5184	4474

prune295.0ms (6.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	107	2	109

Merged error: 0.0b

Counts

109 → 2

Compiler

Compiled 5844 to 3899 computations (33.3% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (/.f64 (+.f64 (.f64 a a) (neg.f64 (pow.f64 a 4))) (-.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (*.f64 3 a))))))
0.1b	(/.f64 (+.f64 (*.f64 a a) (neg.f64 (pow.f64 a 4))) (-.f64 1 a))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
1.3b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

rewrite68.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_2509`
30×	`*-un-lft-identity_binary64_2487`
18×	`times-frac_binary64_2493` `add-cube-cbrt_binary64_2522`
12×	`add-exp-log_binary64_2525`
11×	`add-cbrt-cube_binary64_2523`
10×	`pow1_binary64_2548`
8×	`difference-of-squares_binary64_2456`
6×	`associate-/r*_binary64_2431` `add-log-exp_binary64_2526`
4×	`distribute-lft-out--_binary64_2439`
3×	`distribute-rgt-in_binary64_2437` `pow-unpow_binary64_2564` `distribute-lft-in_binary64_2436` `unpow-prod-down_binary64_2566` `prod-exp_binary64_2536` `associate-/l_binary64_2432` `cbrt-unprod_binary64_2520` `pow-prod-down_binary64_2558` `associate-r*_binary64_2427`
2×	`flip--_binary64_2462` `sub-neg_binary64_2480` `cancel-sign-sub-inv_binary64_2453` `associate-/r/_binary64_2433` `flip-+_binary64_2461` `div-sub_binary64_2492` `flip3-+_binary64_2490` `associate-+r+_binary64_2419` `associate-/l/_binary64_2434` `associate-*r/_binary64_2429` `flip3--_binary64_2491`
1×	`pow-exp_binary64_2555` `unswap-sqr_binary64_2455` `-commutative_binary64_2418` `pow-to-exp_binary64_2556` `pow-pow_binary64_2559` `frac-2neg_binary64_2498` `clear-num_binary64_2486` `div-inv_binary64_2484` `+-commutative_binary64_2417` `sum-log_binary64_2578` `unsub-neg_binary64_2481` `div-exp_binary64_2538` `sqr-pow_binary64_2459` `associate-l*_binary64_2428` `unpow2_binary64_2552` `associate-+r-_binary64_2421` `neg-sub0_binary64_2482` `cbrt-undiv_binary64_2521`

Counts

4 → 101

Calls

4 calls:

20.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (/.f64 (+.f64 (.f64 a a) (neg.f64 (pow.f64 a 4))) (-.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (*.f64 3 a))))))
19.0ms	(/.f64 (+.f64 (*.f64 a a) (neg.f64 (pow.f64 a 4))) (-.f64 1 a))
9.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series441.0ms (9.1%)

Counts

4 → 12

Calls

4 calls:

165.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (/.f64 (+.f64 (.f64 a a) (neg.f64 (pow.f64 a 4))) (-.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (*.f64 3 a))))))
147.0ms	(/.f64 (+.f64 (*.f64 a a) (neg.f64 (pow.f64 a 4))) (-.f64 1 a))
68.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
60.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify77.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5123	2857

prune213.0ms (4.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	113	2	115

Merged error: 0.0b

Counts

115 → 2

Compiler

Compiled 5003 to 2849 computations (43.1% saved)

regimes213.0ms (4.4%)

Compiler: Compiled 3108 to 2078 computations (33.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	78	55
1	78	55

end0.0ms (0%)

sample1.1s (23.2%)

Algorithm

1×

intervals

Results

552.0ms	8000×	body	128	valid
1.0ms	8×	body	128	invalid

Compiler

Compiled 583 to 397 computations (31.9% saved)

Details

analyze145.0ms (3%)

sample26.0ms (0.5%)

simplify235.0ms (4.9%)

prune3.0ms (0.1%)

localize17.0ms (0.3%)

rewrite44.0ms (0.9%)

series332.0ms (6.9%)

simplify43.0ms (0.9%)

prune211.0ms (4.4%)

localize23.0ms (0.5%)

rewrite83.0ms (1.7%)

series316.0ms (6.5%)

simplify105.0ms (2.2%)

prune306.0ms (6.3%)

localize23.0ms (0.5%)

rewrite66.0ms (1.4%)

series315.0ms (6.5%)

simplify78.0ms (1.6%)

prune295.0ms (6.1%)

localize21.0ms (0.4%)

rewrite68.0ms (1.4%)

series441.0ms (9.1%)

simplify77.0ms (1.6%)

prune213.0ms (4.4%)

regimes213.0ms (4.4%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.1s (23.2%)

Profiling